Federici, who had battled melanoma for three years, died at Memorial Sloan-Kettering Cancer Center in New York. News of his death was posted late Thursday on Springsteen's official Web site.
He last performed with Springsteen and the band last month, appearing during portions of a March 20 show in Indianapolis.
"Danny and I worked together for 40 years - he was the most wonderfully fluid keyboard player and a pure natural musician. I loved him very much ... we grew up together," Springsteen said in a statement posted on his Web site.
Federici was born in Flemington, N.J., a long car ride from the Jersey shore haunts where he first met kindred musical spirit Springsteen in the late 1960s. The pair often jammed at the Upstage Club in Asbury Park, N.J., a now-defunct after-hours club that hosted the best musicians in the state.
It was Federici, along with original E Street Band drummer Vini Lopez, who first invited Springsteen to join their band.
By 1969, the self-effacing Federici - often introduced in concert by Springsteen as "Phantom Dan" - was playing with the Boss in a band called Child. Over the years, Federici joined his friend in acclaimed shore bands Steel Mill, Dr. Zoom and the Sonic Boom and the Bruce Springsteen Band.
Federici became a stalwart in the E Street Band as Springsteen rocketed from the boardwalk to international stardom. Springsteen split from the E Streeters in the late '80s, but they reunited for a hugely successful tour in 1999.
"Bruce has been supportive throughout my life," Federici said in a recent interview with Backstreets magazine. "I've had my ups and downs, and I've certainly given him a run for his money, and he's always been there for me."
Federici played accordion on the wistful "4th Of July, Asbury Park (Sandy)" from Springsteen's second album, and his organ solo was a highlight of Springsteen's first top 10 hit, "Hungry Heart." His organ coda on the 9/11-inspired Springsteen song "You're Missing" provided one of the more heart-wrenching moments on "The Rising" in 2002.
In a band with larger-than-life characters such as saxophonist Clarence Clemons and bandana-wrapped guitarist "Little" Steven Van Zandt, Federici was content to play in his familiar position to the side of the stage. But his playing was as vital to Springsteen's live show as any instrument in the band.
Federici released a pair of solo albums that veered from the E Street sound and into soft jazz. Bandmates Nils Lofgren on guitar and Garry Tallent on bass joined Federici on his 1997 debut, "Flemington." In 2005, Federici released its follow-up, "Out of a Dream."
Federici had taken a leave of absence during the band's tour in November 2007 to pursue treatment for melanoma, and was temporarily replaced by veteran musician Charles Giordano.
At the time, Springsteen described Federici as "one of the pillars of our sound and has played beside me as a great friend for more than 40 years. We all eagerly await his healthy and speedy return."
Besides his work with Springsteen, Federici played on albums by an impressive roster of other artists: Van Zandt, Joan Armatrading, Graham Parker, Gary U.S. Bonds and Garland Jeffreys.